Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-17T23:12:44.457Z Has data issue: false hasContentIssue false
  • English
  • Français

Towards enhancing and delaying disturbances in free shear flows

Published online by Cambridge University Press:  26 April 2006

W. O. Criminale ,
T. L. Jackson  and
D. G. Lasseigne
W. O. Criminale
Affiliation:
Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA
T. L. Jackson
Affiliation:
Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, Hampton, VA 23681-0001, USA
D. G. Lasseigne
Affiliation:
Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The family of shear flows comprising the jet, wake, and the mixing layer are subjected to perturbations in an inviscid incompressible fluid. By modelling the basic mean flows as parallel with piecewise linear variations for the velocities, complete and general solutions to the linearized equations of motion can be obtained in closed form as functions of all space variables and time when posed as an initial-value problem. The results show that there is a continuous spectrum as well as the discrete spectrum that is more familiar in stability theory and therefore there can be both algebraic and exponential growth of disturbances in time. These bases make it feasible to consider control of such flows. To this end, the possibility of enhancing the disturbances in the mixing layer and delaying the onset in the jet and wake is investigated. It is found that growth of perturbations can be delayed to a considerable degree for the jet and the wake but, by comparison, cannot be enhanced in the mixing layer. By using moving coordinates, a method for demonstrating the predominant early and long time behaviour of disturbances in these flows is given for continuous velocity profiles. It is shown that the early time transients are always algebraic whereas the asymptotic limit is that of an exponential normal mode. Numerical treatment of the new governing equations confirm the conclusions reached by use of the piecewise linear basic models. Although not pursued here, feedback mechanisms designed for control of the flow could be devised using the results of this work.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 294 , 10 July 1995 , pp. 283 - 300
Copyright
© 1995 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Betchov, R. & Criminale, W. O. 1967 Stability of Parallel Flows. Academic.
Bun, Y. & Criminale, W. O. 1994 Early period dynamics of an incompressible mixing layer. J. Fluid Mech. 273, 31–82.Google Scholar
Criminale, W. O. & Drazin, P. G. 1990 The evolution of linearized perturbations of parallel flows. Stud. Appl. Maths 83, 123–157.Google Scholar
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
Ellingsen, T. & Palm, E. 1975 Stability of linear flow. Phys. Fluids 18, 487–488.Google Scholar
Gustavsson, L. H. 1979 Initial-value problem for boundary layer flows. Phys. Fluids 22, 1602–1605.Google Scholar
Kelvin, Lord 1887 Phil. Mag. 24, 188–196.
Orr W. M.'F. 1907a The stability or instability of the steady motions of a perfect liquid and a viscous liquid. Part I.. Proc. R. Irish Acad. 27, 9–68.Google Scholar
Orr W. M.'F. 1907b The stability or instability of the steady motions of a perfect liquid and a viscous liquid. Part II.. Proc. R. Irish Acad. 27, 69–138.Google Scholar